The generalized solutions of a certain n th order Cauchy-Euler equation

Amornrat Sangsuwan; Kamsing Nonlaopon; Somsak Orankitjaroen

doi:10.1142/S1793557120500473

The generalized solutions of a certain n th order Cauchy-Euler equation

Amornrat Sangsuwan
, Kamsing Nonlaopon
, Somsak Orankitjaroen

Faculty of Science, Khon Kaen University
CHE
Mahidol University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

In this paper, we propose the generalized solutions of a certain nth order Cauchy-Euler equation of the form tny(n)(t) + tn-1y(n-1)(t) + ⋯ + ty′(t) + my(t) = 0, where m and n are any integers with n ≥ 2, and t a using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of m. At the end of the paper, we give some examples showing the types of solutions.

Original language	English
Article number	2050047
Journal	Asian-European Journal of Mathematics
Volume	13
Issue number	2
DOIs	https://doi.org/10.1142/S1793557120500473
Publication status	Published - 1 Mar 2020
Externally published	Yes

Keywords

Cauchy-Euler equation
Dirac delta function
Generalized solution
Laplace transform
distributional solution

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10.1142/S1793557120500473

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abstract = "In this paper, we propose the generalized solutions of a certain nth order Cauchy-Euler equation of the form tny(n)(t) + tn-1y(n-1)(t) + ⋯ + ty′(t) + my(t) = 0, where m and n are any integers with n ≥ 2, and t a using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of m. At the end of the paper, we give some examples showing the types of solutions.",

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AU - Sangsuwan, Amornrat

AU - Nonlaopon, Kamsing

AU - Orankitjaroen, Somsak

PY - 2020/3/1

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N2 - In this paper, we propose the generalized solutions of a certain nth order Cauchy-Euler equation of the form tny(n)(t) + tn-1y(n-1)(t) + ⋯ + ty′(t) + my(t) = 0, where m and n are any integers with n ≥ 2, and t a using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of m. At the end of the paper, we give some examples showing the types of solutions.

AB - In this paper, we propose the generalized solutions of a certain nth order Cauchy-Euler equation of the form tny(n)(t) + tn-1y(n-1)(t) + ⋯ + ty′(t) + my(t) = 0, where m and n are any integers with n ≥ 2, and t a using Laplace transform technique. We find that the types of solutions either distributional solutions or weak solutions, depend on the values of m. At the end of the paper, we give some examples showing the types of solutions.

KW - Cauchy-Euler equation

KW - Dirac delta function

KW - Generalized solution

KW - Laplace transform

KW - distributional solution

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JO - Asian-European Journal of Mathematics

JF - Asian-European Journal of Mathematics

IS - 2

M1 - 2050047

ER -

The generalized solutions of a certain n th order Cauchy-Euler equation

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Keywords

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